Rewrite as a simplified fraction. ${0.\overline{18} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 18.1818...\\ 1x &= 0.1818...\end{align*}}$ Subtracting the two equations, we have: ${99x = 18}$ ${x = \dfrac{18}{99}} $ ${x = \dfrac{2}{11}} $